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Clearly an exacting experiment is called for, of extended duration. Gary, would you kindly present us with photographic evidence of the aforementioned quartz watches, DUCT TAPED to your stomach.

Make sure to tape them on upside-down, so when you look down at your stomach, the numbers are the right side up! I am sure the list will require photographic evidence of you all contorted up, just trying to decipher
the digits!

As usual, George is right again (mostly.) I will keep the watches is the freezer for a while longer but even the short time period so far has shown a considerable change in the rates of the watches. The temperature in the freezer has been in the range
of 1º F to - 10ºF, say an average of about -5º about 80ºF (45º C) lower than before. In the 10.3 hours that they have been in the freezer so far they have lost 1.5, 1.5 and 1.0 seconds corresponding to daily rates of -3.5, -3.5 and -2.3 seconds per day. Based
on their performance in the past they should have each gained some small amount but that is lost in the imprecision of my reading of the watches compared to the WWV time signals, about one half second resolution. George predicted a change of rate of 7 or 8
seconds per day with this change in average temperature but the observed change in the short period so far is only about half of that but this might be masked by the imprecision of the readings also.

Apache Runner provided a formula for the change in frequency of the watch crystal as:

"Quartz crystals have the great advantage that they have very little temperature dependence. Typically, they're fabricated to have a minimum sensitivity to temperature around 25 degrees C.

As I recall, the dependence is roughly a quadratic, and goes like the square of the difference in temperatures - departures from 25 degrees C. The coefficient is something like 0.04 ppm/(degrees C)**2

So, at freezing, one might expect 25 ppm shift, which is 2 seconds per day - pretty significant, if I consider that my typical systematic drift is 0.1 seconds per day at standard temp's."

Using this formula would also predict a change of rate of 7 seconds per day which hasn't happened so for but we will follow it for a while longer. Assuming that this formula is approximately correct, a change of average temperature of 5ºC would predict a change
of rate of .09 seconds per day and a change of 10ºC would cause a change of .35 seconds per day.

So I disagree with George to the extent that if the watches are kept in an insulated box, to limit the effect of diurnal changes in cabin temperatures, then the change in rate will only happen based on long term changes in ambient temperature, say on a cruise
from the Caribbean to England. But, if the cabin is kept in a range of temperatures which are habitable for humans then the change of rates can be kept to a small number.

And my advice for anyone wanting to use these watches for celestial navigation on an expedition across Antarctica is to duct tape them to your stomach under all of your clothes which will turn you into a temperature stabilizing "oven" for the crystals. Off
course, prior to your expedition, you must determine their rates by wearing them taped to your stomach for some reasonable period of time.

gl

George Huxtable wrote:

Gary wrote-
"So I have decided to extend my experiment. I have just placed all thee
watches in my freezer which is at -7º right now (along with the recording
thermometer) and will see what the rates are after three weeks and I will
report back then."
Let me predict that Gary will then see all three watches losing about 7 or 8
seconds a day (if he's talking about temperatures measured in Fahrenheit
degrees).
Quartz crystal frequencies do change with temperature, but not necessarily
in a linear way. By choosing the way that the crystal is cut, it's possible
to make its resonant frequency change parabolically with temperature, such
that it's a maximum at a convenient ambient temperature (such as 25º C) and
falls away either side, at temperatures that are higher or lower. This means
that it's most constant over the range of ambient temperatures that a watch
has to live in. (I understand that in some circumstances crystal oscillators
can be made to give a point-of-inflection rather that a maximum frequency at
that temperature, which can extend the useful temperature range somewhat
further.)
But, as with any such parabolic variaition, once you get away from the
optimum temperature, the dependence on temperature becomes more severe.
In the freezer, Gary will be operating his watches at about 47ºC below their
optimum temperature of 25ºC. Similarly, I would expect that if he operated
them at 47ºC, above it, at 72ºC, if they will stand that (he may be
understandably reluctant to try), then I would expect them to run similarly
slow, 7 or 8 seconds a day.
Wearing a watch on the wrist well help to keep its temperature up in the
daytime, but won't help much if it's taken off at night, in many
environments (such as small craft) that don't expect central heating. Nor
will "wrapping the watch in blankets"; an inanimate object will derive
little benefit from such attentions, much less than Gary or I would. They
will only delay changes in ambient temperature reaching the watch; but they
will get to it in the end.
Gary refers to the use of a "crystal oven", to compensate for changes in
ambient temperature. Indeed, that's a viable technology, that I was using
for precise time measurement, 40 years ago. The crystal is put into a little
insulated housing containing a heating element and a temperature sensor,
with feedback to keep the crystal's temperature constant. It's done that
way, because it's so much easier to heat things above ambient temperature
than to cool them below it. An operating temperature is chosen that's
higher than the environment is ever expected to reach (40ºC, say) and a
crystal is chosen which has its optimum temperature to correspond. Such an
oscillator has its own "warm-up" period, after switch-on, until the oven
stabilises. This technique is seldom used for anything portable, unless
unavoidable, because of the power consumption by the oven.
George.
contact George Huxtable, at george{at}hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
=====================
----- Original Message -----
From: "Gary LaPook" <glapook---.net>
To: <navlist@fer3.com>
Sent: Wednesday, September 16, 2009 1:34 AM
Subject: [NavList 9757] Re: How Many Chronometers?
I remember when I first got involved with radios back in the '60s that I
coveted a high end radio that had an "oven" to keep the oscillator crystal
at a constant temperature to keep the radio frequency from drifting as the
crystal changed temperature. I now think, however, that that was mainly "a
self inflicted wound" due to the tubes (valves) in the radios having
"heaters" to "boil off" electrons from the cathodes in order to make the
tubes function which caused the radios to change temperature a lot and to
run quite hot. The young guys won't remember waiting for a radio to "warm
up" before it would start working but us old timers will remember the orange
glow coming out of the back of the radio from the glow of the "heaters" in
each tube. I clearly remember warming my hands on cold nights over the hot
radio.
I now wonder if the much less extreme swings of temperature that would be
expected in a wrist watch, or by a watch kept in an insulated box below
decks, would make a large change in the watch crystals' resonant frequency
affecting their rates in any significant way.
So I have decided to extend my experiment. I have just placed all thee
watches in my freezer which is at -7º right now (along with the recording
thermometer) and will see what the rates are after three weeks and I will
report back then.
gl
--- On Tue, 9/15/09, Werner Luehmann <wksj.luehmann{at}t-online.de> wrote:
From: Werner Luehmann <wksj.luehmann{at}t-online.de>
Subject: [NavList 9737] Re: How Many Chronometers?
To: navlist@fer3.com
Date: Tuesday, September 15, 2009, 10:21 AM
Sorry Gary, wrong conclusion. The problem with quartz watches (or any quartz
driven oscillator) is their temperature dependance. Only under a constant
temperature you would get constant "rates". For example, in high class
radios the quartz is kept at a constant temperature higher than the ambient
temperature in order to ensure frequency stabilty. In wrist watches
compensating electronic devices can be used. But this is expensive and not
found in 17 Dollars pieces, if at all.
So unfortunately this cheap solution doesn't work for us.
B.T.W.: I have some nice digital (and not too cheap) stopwatches (made by
the
German manufacturer "Hanhart") that elected to adjust their rates according
to the year's season ;-)
Werner
Am Dienstag, 15. September 2009 11:22:33 schrieb Gary LaPook:

Based on our discussion, I became curious about the accuracy of digital
watches and their suitability for use as chronometers so I went to my
local TARGET store and purchased three identical watches for $17.00
each, the cheapest that they had. I set them and let them run for a few
days and, as I expected, they each had different rates. Based on this I
labeled them "A", "B", and "C" in the order of their rates starting with
the slowest. I then reset them to UTC at 0121 Z on May 28, 2009. I
checked them against UTC from WWV eleven days later on June 8th and
found that they were all running fast by 2, 4 and 7 seconds respectively
and I worked out their daily rates as .1818, .3636, and .6363 seconds
per day, respectively.
On July 11th, 44 days after starting the test, the watches were fast by
9, 17 and 28 seconds. Using the rates determined in the first 11 days
the predicted errors would have been 8, 16 and 28 amounting to errors in
prediction of 1, 1, and 0 seconds. If using these three watches for a
chronometer we could average the three errors and end up with only a .66
second error in the UTC determined by applying the daily rates to the
three displayed times after 33 days from the last check against WWV
which took place on June 8th.
I determined new rates now based on the longer 44 day period of .2045,
.3864 and .6363 seconds per day, respectively.
On September 15th at 0800 Z (per WWV), 110 days after starting the
test, I took a photo of the watches which I have attached. The photo
shows the watches fast by 21, 41 and 69 seconds but by carefully
comparing them individually with the ticks from WWV the estimated actual
errors are 21.5, 41.8 and 69.0 seconds. Using the 44 day rates, the
predicted errors are 22.5, 42.5, and 70 seconds giving the errors in the
predictions of 1.0, 0.7 and 1.0 seconds which, if averaged, would have
caused a 0.9 second error in the computed UTC after 66 days from the
last check against WWV on July 11th.
If, instead, I used the 11 day rates then the predicted errors would
have been 20.0, 40.0, and 70.0 seconds which would result in errors of
prediction of -1.5, -1.8, and 1.0 which, if averaged, would cause and
error in the computed UTC of -0.6 seconds after 99 days from the last
check against WWV which would have been on June 8th in this example.
From this experiment it appears that fifty one dollars worth of cheap
watches would give you a perfectly adequate chronometer.
gl

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